Abstract
A number of recent experimental measurements suggest the possibility of a breakdown of lepton ($\ell$) universality in exclusive $b \to c \ell \nu_\ell$ semileptonic meson decays. We analyze the full differential decay rates for several such processes, and show how to extract combinations of the underlying helicity amplitudes that are completely independent of $m_\ell$. Ratios of these combinations for different $\ell$ (as well as some combinations for a single value of $\ell$) therefore equal unity in the Standard Model and provide stringent tests of lepton universality. Furthermore, the extractions assume the form of weighted integrals over the differential decay rates and therefore are useful even in situations where data in some regions of allowed phase space may be sparse.
Highlights
The standard model (SM) has historically worked extremely well, but many compelling reasons lead one to expect the existence of beyond-standard-model (BSM) physics
In this paper we have constructed robust tests of generic lepton-universality violations in semileptonic decays that are independent of knowledge of the transition form factors between hadronic states, for a pseudoscalar meson decaying to a hadron H
Starting from the fully differential cross section decomposed into the helicity basis, one can construct weight functions that project onto specific combinations, labeled by i, of helicity amplitudes
Summary
The standard model (SM) has historically worked extremely well, but many compelling reasons lead one to expect the existence of beyond-standard-model (BSM) physics. Recent RðDÃÞ results from LHCb [8] and Belle [18] suggest a value more consistent with theory, but at present are unincorporated into the global fit. This tension could be due to statistical fluctuations and/or some subtle systematic experimental bias. If, these results are early signals of BSM physics, a natural explanation could be a breakdown of lepton universality, i.e., some process by which the τ and ντ couple to the decaying B or Bc meson differently than do a μ and νμ.
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